The Doe family had a rectangular garden with a 58-foot perimeter. They reduced the length by 7 feet and decreased the width to be half as wide as it was originally. This resulted in a garden with a 34-foot perimeter. What is the area of the new smaller garden?

To derive the demand function from the given utility function and endowment, we need to determine the optimal allocation of goods that maximizes utility. The utility function is U(x, y) = -e^(-x) - e^(-y), and the initial endowment is (1, 0).

To derive the demand function, we need to find the optimal allocation of goods x and y that maximizes the given utility function while satisfying the endowment constraint. We can start by setting up the consumer's problem as a utility maximization subject to the budget constraint. In this case, since there is no price information provided, we assume the goods are not priced and the consumer can freely allocate them.

The consumer's problem can be stated as follows:

Maximize U(x, y) = -e^(-x) - e^(-y) subject to x + y = 1.

To solve this problem, we can use the Lagrangian method. We construct the Lagrangian function L(x, y, λ) = -e^(-x) - e^(-y) + λ(1 - x - y), where λ is the Lagrange multiplier.

Taking partial derivatives of L with respect to x, y, and λ, and setting them equal to zero, we can find the values of x, y, and λ that satisfy the optimality conditions. Solving the equations, we find that x = 1/2, y = 1/2, and λ = 1. These values represent the optimal allocation of goods that maximizes utility given the endowment.

Therefore, the demand function derived from the utility function and endowment is x = 1/2 and y = 1/2. This indicates that the consumer will allocate half of the endowment to each good, resulting in an equal distribution.

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Answer:

-x2 + 50 = 25

5x<0

2x <10

Step-by-step explanation:

I hope the answer satisfies you

Answer:

2 and 3

Step-by-step explanation:

Sqrt(5) will lie between the square root of the perfect square before 5 and the square root of the perfect square after 5

Perfect square before 5 = 4

Perfect square after 5 = 9

sqrt(4) and sqrt(9)

2 and 3

As per the boundary, the steady state solution of the problem is u(x,1)

The boundary conditions of a PDE are crucial in determining the behavior of the solution.

With this new setup, we can write u(x,1) = Usteady state(x) + U(x,0). This equation tells us that the original solution u(x,1) is equal to the steady-state solution plus the transient solution U(x,0).

The transient solution U(x,t) describes how the system evolves from the initial condition to the steady-state solution over time.

To find the steady-state solution, we first need to solve the homogeneous PDE for U(x,t), which is given by U, = Uxx, with the boundary conditions U(0,t) = 0 and U(1,t) = 0, and the initial condition U(x,0) = Usteady state(x) - u(x,1).

Once we have found U(x,t), we can add it to the steady-state solution Usteady state(x) to obtain the original solution u(x,1).

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Answer:

16537.5

Step-by-step explanation:

4.5% of 13500 = 607.5

607.5 x 5 = 3037.5

3037.5 + 13500 = 16537.5

฿₤₦

Cost of one movie = $3.25

Cost of one video game = $5.5

Let the rental cost of each movie be "x"

Let the rental cost for each video be "y"

If in one month Juan rented 2 movies and 3 video games for a total of $23, this can be expressed as:

If in another month he rented 4 movies and 8 video games for a total of $57, this can be expressed as:

Solve both equations simultaneously using the elimination method.

2x + 3y = 23 .................................... 1 * 2

4x + 8y = 57 .................................... 2 * 1

________________________________________

4x + 6y = 46

4x + 8y = 57

Subtract both equations

6y - 8y = 46 - 57

-2y = -11

y = 11/2

y = $5.5

Substitute y = 5.5 into equation 1

From equation 1, 2x + 3y = 23

2x + 3(5.5) = 23

2x + 16.5 = 23

2x = 23 - 16.5

2x = 6.5

x = 6.5/2

x = $3.25

Hence the cost for each movie is $3.25 and the cost of each video game is $5.5

The missing degrees in the circle are 260 degrees.

What is circle ?

A circle is a geometrical shape that represents a set of points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the diameter of the circle is the distance across its widest point, passing through the center.

To find the missing degrees in the circle, we need to use the fact that the sum of the central angles in a circle is equal to 360 degrees.

In this circle, we have two central angles: one measuring 100 degrees and the other measuring x degrees. We also know that the sum of these two central angles is equal to 360 degrees.

Therefore, we can set up the following equation:

100 + x = 360

To solve for x, we can subtract 100 from both sides:

x = 260

Therefore, the missing degrees in the circle are 260 degrees.

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The expression V − E + F is an illustration of the Euler's formula.

The expression V − E + F is always 2

The equation is given as:

V - E + F = 2

Where:

According to the Euler's formula, the relationship between V, E and F is:

V + F = 2 + E

Subtract E from both sides

V - E + F = 2

Hence, the expression V − E + F is always 2

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Sorry for the late answers, but the answers are...

6

3.40

1.61

I know this because I had this problem and I got it correct. The screenshot attached is proof that the answers are correct

Answer:

There are 6 observed toll fee values.

It costs 3.40 to travel 76 miles.

The predicted value for traveling 30 miles is 1.61

Step-by-step explanation:

The expression  x²-6x+9 is equal to the expression (x-3)², option A is correct.

The given expression is x²-6x+9

x is the variable in the expression

Plus and minus are the operators

We have to factor the expression

x²-6x+9

x²-3x-3x+9

x(x-3)-3(x-3)

(x-3)(x-3)

x²-6x+9 is equal to (x-3)²

(x-3)²

Hence, the expression  x²-6x+9 is equal to the expression (x-3)², option A is correct.

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Answer:

The Champs with a mean of about 66.4 inches.

Explanation:

Champs:

62, 69, 65, 68, 60, 70, 70, 58, 67, 66, 75, 70, 69, 67, 60

The mean of a set of numbers is the sum divided by the number of terms, which in this situation for the champs is 66.4 inches.

Super Stars:

66, 66, 66, 63, 63, 63, 65, 65, 65, 64, 64, 64, 58, 58, 58

The mean of a set of numbers is the sum divided by the number of terms, which in this situation for the champs is 63.2 inches.

Results:

So from the data of both of them, the Champs have a larger average than the super stars (the mean of numbers means the average) so it would be 66.4 inches.

The Western Allies, carry out the protection of democratic states from the perceived threat of Communist occupation (see the part on the Cold War and European integration)

began to begin a set of international organizations so that national governments could work jointly to resolve common problems on issues ranging from defense and security to moral trade to rebuild European nations physically and economically shattered by the Second World War.

Because so much had been demolished during the war, many European countries were heavily in debt to the United States and could not bear to rebuild.

There was a scarcity of food and raw materials; thousands of refugees were still those do not have homes.

Due to these problems, there were almost no jobs and unemployment was high.

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In order to determine how much does Allison pay for her utilitites, it is only necessary to calculate the percentage associated to utilities, given in the table (2.3%) of the Allison's earns ($6,500).

For calculating the 2.3% of 6,500, you simply multiply (2.3/100) by 6,500, just as follow:

(2.3/100)(6,500) = 149.5

Then, the 2.3% of $6,500 is $149.5. Hence, Allison pay $149 for her utilities

Based on the given data set, we can only determine a single mode, which is 4.

To determine the mode(s) of the given data set representing the number of new seeds planted in the garden for 15 varieties of sunflower, we need to find the value(s) that appear most frequently.

Here are the steps to find the mode(s):

1. Organize the data set in ascending or descending order to make it easier to identify repeated values. For example, let's say the data set is: 4, 5, 6, 2, 7, 4, 3, 5, 2, 4, 6, 4, 7, 3, 4.

2. Count the frequency of each value in the data set. In our example, we have:

  - Value 2 appears 2 times.
  - Value 3 appears 2 times.
  - Value 4 appears 5 times.
  - Value 5 appears 2 times.
  - Value 6 appears 2 times.
  - Value 7 appears 2 times.

3. Identify the value(s) with the highest frequency. In our example, the value 4 appears most frequently with a count of 5 times.

Therefore, the mode of the data set is 4, indicating that the number 4 is the most common value among the number of new seeds planted in the garden for the 15 varieties of sunflower.

It's important to note that in some cases, there may be multiple modes if two or more values have the same highest frequency.

However, based on the given data set, we can only determine a single mode, which is 4.

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Answer: 88 1/2

Step-by-step explanation:

easy

Answer:

89

Step-by-step explanation:

Answer:

Step-by-step explanation:

cos theta is 2/3 because  cos means reciprocal of sec

Answer:

option C

Step-by-step explanation:

\(sec\theta = \frac{1}{cos\theta}\\\\\frac{3}{2}= \frac{1}{cos\theta}\\\\cos\theta = \frac{1}{\frac{3}{2}} = \frac{2}{3}\)

From the question, the sum of each of the geometric sequence are;

1)  31 3/4

2) 340

3) 11/16

4) -6, 12, -24

We have that;

Sn = a(1 -\(r^n\))/1 - r

Sn = 16(1 \(- (1/2)^7\))1 - 1/2

Sn = 16(1 - 1/128)/1/2

Sn = 16(127/128) * 2

Sn = 31 3/4

2) Un = a\(r^n\) -1

256 = \(4(4)^n-1\)

64 =\(4^n-1\)

\(4^3 = 4^n-1\)

n = 4

Sn= \(4(4^4 - 1)\)/4 - 1

Sn = 340

3) Since we have a5 then n = 5

Sn = 1(1 - (\(-1/2)^5\))/1 -(-1/2)

Sn = 33/32 * 2/3

= 11/16

4) 30= a(1 -\((-2)^4\))/1 - (-2)

30 = a(-15)/3

30 = -5a

a = 30/-5

a = -6

Then the first three terms are;

-6, 12, -24

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False, forces created by snow are not typically termed linearly distributed loads.

Forces created by snow are generally referred to as uniformly distributed loads, not linearly distributed loads. A uniformly distributed load applies a constant force per unit length or area over a specific region. In the case of snow, when it covers a surface or exerts pressure on a structure, the weight of the snow is distributed evenly across the surface, resulting in a uniform load.

This means that the force exerted by the snow is relatively consistent over the entire area it covers. On the other hand, a linearly distributed load would vary linearly along the length or area, meaning the force would change in a linear fashion. Snow loads are more accurately described as uniformly distributed loads due to their consistent distribution of force across a given surface or structure.

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Answer:

1/10

Step-by-step explanation:

All spinners have equal areas & circumference on each outcome, so spinning an A is one out of five, or 1/5.  The probability of spinning any number is 1/6.  Since 1, 3, and 5 are all odd numbers, the probability of spinning an odd number is 3/6, or 1/2.

The probability of spinning both spinners successfully (an A AND an odd number) can be found by the product rule, which is the product of the two probabilities, namely 1/5 * 1/2 = 1/10.

Answer:

Pedro had 1,617 base hits.

Step-by-step explanation:

2674 ÷ 2 = 1337

1337 + 280 = 1617

The probability of of a random student having blue eyes and dark hair

 is 35% .

let consider the total students in the school be (U) = 100%

out of them ,

students having blue eyes (A) = 60%

students having  dark hair (B) = 55%

students with neither blue eyes nor dark hair (A∪B)' = 20%

let the students with blue eyes and dark hair be (A∩B) = x %

Then according to the set theorem

U = n(A∪B) + n(A∪B)'

U = n(A) + n(B) - n(A∩B) + n(A∪B)'

100 = 60 + 55 - x +20

∴ x = 60 + 55 +20 - 100

x = 35 %

So the probability of random student having blue eyes and dark hair is 35% .

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Answer:

347/40

Step-by-step explanation:

34.7/4 = 34 7/10 / 4

= 347/10 / 4

= 347/40

It took 1700 J of work to stretch a spring from its natural length of 2 m to a length of 6 m. The spring constant k will be 212.5 N/m.

The potential energy stored in a spring is given by the formula:

PE = (1/2) kx^2

where k is the spring constant, x is the displacement from the equilibrium position, and PE is the potential energy.

In this problem, the spring is stretched from its natural length of 2 m to a length of 6 m, so the displacement is x = 6 m - 2 m = 4 m.

The work done on the spring is equal to the change in potential energy, so:

Work = PE final - PE initial

1700 J = (1/2) k(4² - (1/2) k(0)²

1700 J = 8k

k = 212.5 N/m

Therefore, the spring constant is 212.5 N/m.

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Answer:

15

Step-by-step explanation:

the range is the largest number take away the smallest number

56-41=15

Answer: 92 dollars because 15% divided into 80 is 12 and add 80 to 12 and its 92

Answer:

m=−37

Step-by-step explanation:

34 = -3 + -1m

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add 'm' to each side of the equation.

34 + m = -3 + -1m + m

Combine like terms: -1m + m = 0

34 + m = -3 + 0

34 + m = -3

Add '-34' to each side of the equation.

34 + -34 + m = -3 + -34

Combine like terms: 34 + -34 = 0

0 + m = -3 + -34

m = -3 + -34

Combine like terms: -3 + -34 = -37

m = -37

Answer:

Sample Response:

The negative sign outside the parentheses represents –1. Distribute the –1 to everything inside the parenthesis. Use the addition property of equality first to add 3 to both sides. Then use the division property of equality to divide both sides by -1.

Answer:

\({ \tt{f(x) = 2}} \\ when \: y = 2 \\ { \bf{x = - 0.5}}\)

The volume of gasoline in the tank as a function of time can be determined as,

The time taken to fill the tank can be determined as,

Thus, the requried domain is,

The range of the function can be determined as,

Thus, the above expressions gives the required domain and range of the function.